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The level of water in a vessel falls from a height $64 c m$ to $36 c m$ in 3 minutes as water flows out through a hole in it’s bottom. At the end of next 2 minutes the height of water level in the vessel will be.

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$16.4 c m$

$21.8 c m$

$32.4 c m$

$42.6 c m$

answer is B.

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Detailed Solution

$t α (\sqrt{h 1} - \sqrt{h 2})$

$\frac{3}{2} = \frac{\sqrt{64} - \sqrt{36}}{\sqrt{36} - \sqrt{h}} \Rightarrow \frac{3}{2} = \frac{8 - 6}{6 - \sqrt{h}} = \frac{2}{6 - \sqrt{h}}$

$4 = 18 - 3 \sqrt{h}$

$3 \sqrt{h} = 14 \Rightarrow 9 \times h = 14 \times 14 \Rightarrow h = \frac{14 \times 14}{9}$

$∴ h = \frac{196}{9} = 21.8 c m$

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